Spherical isothermal self-similar shock flows

We explore self-similar dynamical processes in a spherical isothermal self-gravitational fluid with an emphasis on shocks and outline astrophysical applications of such shock solutions. The previous similarity shock solutions of Tsai & Hsu and of Shu et al. may be classified into two types: Class I solutions with downstream being free-fall collapses; and Class II solutions with downstream being Larson‐Penston (LP) type solutions. By the analyses of Lou & Shen and Shen & Lou, we further construct similarity shock solutions in the ‘semicomplete space’. These general shock solutions can accommodate and model dynamical processes of radial outflows (wind), inflows (accretion or contraction), subsonic oscillations and free-fall core collapses all with shocks in various settings such as star-forming molecular clouds, ‘champagne flows’ in H II regions around luminous massive OB stars or surrounding distant quasars, dynamical connections between the asymptotic giant branch phase to the protoplanetary nebula phase with a central hot white dwarf as well as accretion shocks around compact objects such as white dwarfs, neutron stars and supermassive black holes. By a systematic exploration, we are able to construct families of infinitely many discrete Class I and Class II solutions matching asymptotically with a static outer envelope of a singular isothermal sphere; the shock solutions of Tsai & Hsu form special subsets. These similarity shocks travel at either subsonic or supersonic constant speeds. We also construct twin shocks as well as an ‘isothermal shock’ separating two fluid regions of two different yet constant temperatures. Ke yw ords: hydrodynamics ‐ stars: AGB and post AGB ‐ stars: formation ‐ H II regions ‐ planetary nebulae: general ‐ quasars: general.